Examine the triangle below, solve for t, round to the nearest whole number.
T
37
46°
A
84°
t
D
Answers
In the triangle, the nearest whole number of the side t is 28.
What is the sine rule of a triangle?The sine rule states that the ratios of the sides to their corresponding opposite angles are equal to a particular value. This value gives the circumradius of that triangle.
The sum of three angles in a triangle is 180°.
Find the angle ∠T for ∠A=46° and ∠D=84°.
∠A+∠D+∠T=180°
46°+84°+∠T=180°
130°+∠T=180°
∠T=50°
The sine rule for triangle ABC is [tex]\[\frac{a}{{\sin A }} = \frac{{37}}{{\sin B }} = \frac{c}{{\sin C }} = 2R\][/tex], where R is the circumradius and a, b, and c are the opposite sides of the angles ∠A, ∠B, and ∠C, respectively.
On applying the sine rule to triangle ADT, the result becomes [tex]\[\frac{a}{{\sin 46^\circ }} = \frac{{37}}{{\sin 84^\circ }} = \frac{t}{{\sin 50^\circ }} = 2R\][/tex].
Take the equation [tex]\frac{{37}}{{\sin 84^\circ }} = \frac{t}{{\sin 50^\circ }}[/tex] and find t.
[tex]\[\begin{array}{l}t = \frac{{37\sin 50^\circ }}{{\sin 84^\circ }}\\ \approx 28.4997\\ \approx 28\end{array}\][/tex]
Therefore, the nearest round whole number of t is 28.
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Related Questions
Can anyone explain this question about complex numbers ?
Answers
Answer:
Step-by-step explanation:
(a) Using de Moivre's Theorem, we have that:
z^n = cos(nθ) + i sin(nθ)
1/z^n = cos(-nθ) + i sin(-nθ)
So, we can find z^n + 1/z^n as:
z^n + 1/z^n = (cos(nθ) + i sin(nθ)) + (cos(-nθ) + i sin(-nθ)) = 2 cos(nθ)
And z^n - 1/z^n as:
z^n - 1/z^n = (cos(nθ) + i sin(nθ)) - (cos(-nθ) + i sin(-nθ)) = 2i sin(nθ)
(b) To express the equation 2z^4 - 5z^3 + 7z^2 - 5z + 2 = 0 in terms of cos(θ), we can substitute z with cos(θ) + i sin(θ):
2(cos(4θ) + i sin(4θ)) - 5(cos(3θ) + i sin(3θ)) + 7(cos(2θ) + i sin(2θ)) - 5(cos(θ) + i sin(θ)) + 2 = 0
Expanding the right hand side using the trigonometric identities, we get:
2 cos(4θ) - 5 cos(3θ) + 7 cos(2θ) - 5 cos(θ) + 2 = 0
Note that the real and imaginary parts are separate, so we can simplify this equation to a real equation by equating the real and imaginary parts to 0.
(c) To solve the equation 2 cos(4θ) - 5 cos(3θ) + 7 cos(2θ) - 5 cos(θ) + 2 = 0, we can use numerical methods or analytical methods such as the roots of unity.
Once the roots are found, they can be represented on an Argand diagram by plotting the real and imaginary parts of each root as a point in the complex plane. The magnitude of each point represents the magnitude of the complex number, and the argument (angle) represents the argument of the complex number.
In the triangle below, WXY is a equilateral triangle and XZ and WY
Answers
In the given equilateral triangle XYZ the relation which is true is WX = 2WZ. So option C is correct.
What are properties of equilateral triangle?An equilateral triangle is a particular kind of triangle in which the lengths of the three sides are equal. These are a few of its main characteristics:
Congruent angles exist for all three: An equilateral triangle has 60 degrees for each angle.
The three parties all agree: The perimeter of an equilateral triangle is three times the length of any one side because each side is the same length.
For any side, the same line serves as the altitude, median, and angle bisector:
A line segment perpendicular to the other side and drawn from one vertex is the altitude. A line segment called the median is drawn from one vertex to the middle of the other side. The line segment known as the angle bisector divides the angle made up of two sides.
Given that,
The triangle XYZ,
It is known that,
All the sides in the equilateral triangle are equal,
So it can be written as,
⇒ WX = WY = XY
⇒ WY = 2WZ = 2ZY
Therefore,
⇒ WX = 2WZ
Hence, the correct relationship is WZ = 2WZ.
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Answer:
WX=2 times WZ
Step-by-step explanation:
i just took the quiz on apex
7. During a sale at the Honda dealership, Mr. Sherman notices the great 10 points
sales price ($33,500) and purchases two cars for his daughters. What will
he pay in total for the two cars, including 8.875% sales tax?
A. $72,946.25
B. $36,473.13
C. $41,372.50
D. $82,745
Answers
Answer: A
Step-by-step explanation:
First you add up the total prices of both cars
$67,000
Next find 8.875% of that and add to total price of both cars
Answer= $72,946.25
Translate into a variable expression then simplify, a number minus the sum of the number and 6
Answers
Answer:
Translates to x-(x+6) which simplifies to -6
=====================================================
Explanation:
x = some number
x+6 = the sum of x and 6
x-(x+6) = subtract the previous amount from x
x-x-6 .... distribute the negative through to each term
-6
No matter what number you started with, you'll always end up with -6 as the fully simplified answer. The x variables cancel.
Example:
Pick 10 as the starting number. Subtract off 10+6 = 16 to get 10-16 = -6.
Mrs Chong paid for a frying pan that cost $64 with some $10, $5 and $2 notes .If she used a total of 15 notes,how many $5 notes did she use?
Required process!
Thank you
Answers
For every $2 note used, Mrs. Chong used 3/5 of a $5 note. Since she used 15 notes in total, and the number of $2 notes used must be an integer, we can see that she used 10 $2 notes. That means she used 3/5 * 10 = 6 $5 notes.
What is Inequalities?
Inequalities are mathematical statements used to express the comparison between two values. Unlike equalities (e.g., 3 + 4 = 7), which use the "equals" sign (=), inequalities use symbols such as "greater than" (>), "less than" (<), "greater than or equal to" (>=), and "less than or equal to" (<=) to express a relationship between the values.
Let's call the number of $10 notes Mrs. Chong used as "x".
We know the total amount she paid was $64, and the number of notes used was 15, so we can set up an equation:
10x + 5y + 2z = 64
Where "y" is the number of $5 notes used and "z" is the number of $2 notes used. We know that x + y + z = 15 (because this is the total number of notes used).
We can substitute x = 15 - y - z into the first equation:
10(15 - y - z) + 5y + 2z = 64
Expanding the equation:
150 - 10y - 10z + 5y + 2z = 64
Combining like terms:
150 - 5y + 3z = 64
Subtracting 150 from both sides:
-5y + 3z = -86
Dividing both sides by -5:
y - (3/5)z = 17.2
So, for every $2 note used, Mrs. Chong used 3/5 of a $5 note. Since she used 15 notes in total, and the number of $2 notes used must be an integer, we can see that she used 10 $2 notes. That means she used 3/5 * 10 = 6 $5 notes.
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Suppose you have a deck that is 16ft. By 24ft. An 8ft by 4in board costs $7.50. How much will the material costs?
Answers
Answer:
45
Step-by-step explanation:
Five students—the females Ann and Betty and the males Clint, Douglas, and Edward—are rated equally qualified for admission to law school, ahead of other applicants. However, all but two positions have been filled for the entering class. The admissions committee can admit only two more students, so it decides to randomly select two of these five candidates. For this strategy, let of females admitted. Using the first letter of the name to denote a student, the different combinations that could be admitted are (A, B), (A, C), (A, D), (A, E), (B, C), (B, D), (B, E), (C, D), (C, E), and (D, E).
(a)Construct the probability distribution for .
(b)Construct the sampling distribution of the sample proportion of the students selected who are female.
Answers
Answer:
(a) The probability distribution for the number of female students admitted can be calculated as follows:
P(0 female students) = (2C0) × (3C2) / (5C2) = (1) × (3) / (10) = 0.3
P(1 female student) = (2C1) × (3C1) / (5C2) = (2) × (3) / (10) = 0.6
P(2 female students) = (2C2) × (3C0) / (5C2) = (1) × (1) / (10) = 0.1
(b) The sampling distribution of the sample proportion of female students selected can be calculated as follows:
P(p = 0) = 0.3 (for 0 female students)
P(p = 1/2) = 0.6 (for 1 female student)
P(p = 1) = 0.1 (for 2 female students)
Note that the sampling distribution of the sample proportion is a discrete probability distribution with values of 0, 1/2, and 1, and corresponding probabilities 0.3, 0.6, and 0.1, respectively.
Complete the sentence below.
0.075 is a hundred times smaller than
Answers
Answer:
0.0075
Step-by-step explanation:
the preimter of a rectangel measures 78 centimterers the measure of the with is 15 cenimeters what is the area of the rectangel
Answers
Answer:
360 cm^2
Step-by-step explanation:
The length of the rectangle can be found using the formula for perimeter:
Perimeter = 2 * (length + width)
Rearranging the equation, we can solve for the length:
length = (Perimeter - 2 * width) / 2
Plugging in the given values:
length = (78 - 2 * 15) / 2 = (78 - 30) / 2 = 48 / 2 = 24 cm
Next, the area of the rectangle can be found using the formula:
Area = length * width
Plugging in the given values:
Area = 24 * 15 = 360 cm^2
Will is moving from Boston to Philadelphia which is 300 miles away. He is traveling at an
Answers
Write System of Equations from Context
Kennedy has $0.81 worth of pennies and nickels. She has 9 more nickels than
pennies. Write a system of equations that could be used to determine the number of
pennies and the number of nickels that Kennedy has. Define the variables that you
use to write the system.
Let __=_________
Let__=___________
System of Equations:
_________________
_________________
Answers
Let n = the number of nickels Kennedy has
Based on the information given, we can write the following two equations:
The total value of pennies is 0.01p
The total value of nickels is 0.05n
Kennedy has 9 more nickels than pennies, so we can write: n = p + 9
So, the system of equations is:
0.01p + 0.05n = 0.81
n = p + 9
This system of equations can be used to determine the number of pennies and nickels Kennedy has.
PLEASE HELP ASAP IF YOU HELP I WILL GIVE BRANLIST AND BUT ONLY IF YOUR RIGHT BUT ONLY IF YOUR RIGHT. A set of 3 cards, spelling the word ADD, are placed face down on the table. Determine P(D, D) if two cards are randomly selected with replacement.
OPTIONS
1/3
2/3
2/6
4/9
Answers
Answer:
im pretty sure it is 4/9
Step-by-step explanation:
From the question, we are to determine the probability of selecting two cards with D and D
From the formula for probability, we have that
P(D) = Number of favorable outcomes to D / Total number of possible outcomes
From the given information,
Number of favorable outcomes to D = 2
Number of possible outcomes = 3
Thus,
P(D) = 2/3
Then,
The probability of selecting two cards that have D and D with replacement is
P(D, D) = P(D) × P(D)
P(D, D) = 2/3 × 2/3
P(D, D) = 4/9
Hence, the probability is 4/9.
The ratio of boys to girls at the park is 4 to 5. How many boys are at the park if there are 45 girls at the park.
Responses
A 30
B 36
C 42
D 48
Answers
Answer:
Step-by-step explanation:
B
What are the quotient and remainder of (3x^4+ 2x² - 6x + 1) + (x + 1)?
Answers
Answer:
The quotient is 3x^3 + 2x and the remainder is 0.
Step-by-step explanation:
Quotient: 3x³ + 2x
Remainder: -5
Answer:
3x^3 - 3x^2 + x - 1
x + 1 | 3x^4 + 2x^2 - 6x + 1
- (3x^4 + 3x^3)
---------------
-x^3 - 6x + 1
- (-x^3 - x^2)
-------------
-5x^2 - 6x + 1
-(-5x^2 - 5x)
------------
-x + 1
Therefore, the quotient is 3x^3 - 3x^2 + x - 1, and the remainder is -x + 1.
A designer creates a drawing of a triangular sign on centimeter grid paper for a new business. The drawing has sides measuring 3 cm, 4 cm, and 5 cm, and angles measuring 37°, 53°, and 90°. To create the actual sign shown, the drawing must be dilated using a scale factor of 80.
Answers
Answer:
240 cm, 320 cm, 400 cm
Step-by-step explanation:
The drawing length multiplied by the scale factor gives the real length.
3 cm × 80 = 240 cm
4 cm × 80 = 320 cm
5 cm × 80 = 400 cm
Answer: 240 cm, 320 cm, 400 cm
Use the information provided to write the equation of the circle. Center: (-8,11) Radius:2
Answers
Use the information provided to write the equation of the circle Center (-8, 11) Radius is 2 is equal to (x + 8)² + (y - 11)² = 4.
What is equation of the circle?
To write the equation of a circle, we need to know its center and radius. If we have the center at point (a, b) and the radius is r, the equation of the circle is:
(x - a)² + (y - b)² = r²
If you have the specific values of a, b, and r, you can plug them into this equation to get the equation of the circle.
The general equation of a circle with center (h, k) and radius r is:
(x - h)² + (y - k)²= r²
Using the given information, we can substitute the values into the equation:
(x - (-8))² + (y - 11)² = 2²
Simplifying, we get:
(x + 8)² + (y - 11)² = 4
Therefore, the equation of the circle with center (-8, 11) and radius 2 is:
(x + 8)² + (y - 11)² = 4
This equation represents all the points that are 2 units away from the center (-8, 11).
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Question 3 of 5
Solve 3x + 6 = 21.
A. x=7
B. x=5
C. x=8
D. x=9
Answers
Answer:
B. x=5
Step-by-step explanation:
3x + 6 = 21
Subtract 6 from both sides.
3x = 15
Divide both sides by 3.
x = 5
Answer: B. X=5
Step-by-step explanation:
3x+6=21
subtract 6 on both sides
3x=15
divide by 3 on both sides
x=5
Two angles are supplementary angles if the sum of their measures is 180°.
Find two supplementary angles such that the measure of the first angle is 26° less than
three times the measure of the second.
The measure of the first angle is____ft.
Answers
The measure of the first angle is 128. 5 degrees
How to determine the angleFrom the information given, we have that;
The two angles are supplementaryThe sum up to 180 degreesThe first angle is 3x - 26Let the second angle be x
We have the representation as;
3x - 26 + x = 180
collect the like terms, we get;
3x + x = 180 + 26
Add or subtract the like terms
4x = 206
Make 'x' the subject of formula by dividing by the coefficient of x, we get;
x = 206/4
divide the values
x = 51.5 degrees
Then, the angle is 128 .5 degrees
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What is the percent increase from 2000 of 5.53 and 2010 of 22.5 . Round to nearest tenth of a percent
Answers
There was a 305.1% increase in the value from 2000 to 2010.
What is Percent?
To compute a percentage, divide the value by the entire amount and multiply the result by 100.
To calculate the percent increase, we need to determine the difference between the two values and divide it by the original value, then multiply by 100 to express it as a percentage.
For the year 2000:
Percent increase = (22.5 - 5.53) / 5.53 * 100 = 305.05%
And rounded to the nearest tenth of a percent, this would be 305.1%.
So, There was a 305.1% increase in the value from 2000 to 2010.
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HELPP ASAP
suppose
Find the value
Answers
Answer:
C, I did the math
hope this helps
Let f(x) = x2 − 2x + 1. Find the inverse function of f by identifying an appropriate restriction of its domain.
Answers
Answer: [tex]f^{-1} (x) = \sqrt{x} +1[/tex]
Step-by-step explanation:
[tex]y = x^2 - 2x + 1[/tex]
We know straight away the inverse will be a square root function. We also know that this inverse will have a restriction on the domain, (because you can only take the square root of a positive number).
So, to find the inverse, first we'll switch the x and y and solve for y:
[tex]x = y^2 - 2y +1[/tex]
[tex]x = (y-1)^2[/tex], (factor!)
±[tex]\sqrt{x} = y - 1[/tex]
So, the inverse "function" is:
[tex]f^-1(x)[/tex] = ±[tex]\sqrt{x} +1[/tex]
But theres an issue here!
If we tried graphing this, this "function" would not pass the vertical line test, so its not really a function at all!
We need to restrict the domain to only include the values that are above the x axis.
So our final inverse function is:
[tex]f^{-1} (x) = \sqrt{x} +1[/tex]
Let (8,-6) be a point on the terminal side of an angle 0 in standard position. Find the exact value of cos 0.
Answers
The exact value of cosine is 4/5
How to determine the exact value of cosineFrom the question, we have the following parameters that can be used in our computation:
(8,-6) be a point on the terminal side of an angle
Using the above as a guide, we have the following:
Cos(angle) = x/(√x² + y²)
In this case
x = 8 and y = -6
substitute the known values in the above equation, so, we have the following representation
Cos(angle) = 8/(√8² + (-6)²)
So, we have
Cos(angle) = 8/10
Simplify
Cos(angle) = 4/5
Hence, the value is 4/5
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I’m setting up his latest wiring job an electrician out the following lengths of wire 272 946 662 28 23 and 856ft find the total length of wire used
Answers
Answer:
2787
Step-by-step explanation:
add them all together
The expression (ax3 + bx2 - 5x + 2a) is exactly divisible by (x2 - 3x - 4). Calculate the value of 'a' and 'b' and factorise the expression completely.
Answers
If the expression be x² - 3x - 4 then the factorize term be (x - 4)(x + 1).
What is meant by expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
If the expression, ax³ + bx² - 5x + 2a is exactly divisible by x² - 3x - 4, then it is also divisible by both x - 4 and x + 1
If f(x) = ax³ + bx² - 5x + 2a, then f(4) = f(-1) = 0 by the factor theorem.
Hence, a(4)³ + b(4)² - 5(4) + 2a = 0 and
a(-1)³ + b(-1)² - 5(-1) + 2a = 0
⇒ so, 66a + 16b = 20 and a + b = -5
33a + 8b = 10 ...(1)
a + b = -5 ...(2)
simplifying the above (1) and (2), we get
33a + 8(-5 - a) = 10
i.e. 25a - 40 = 10
so, a = 2 ⇒ b = -7
Therefore, the function be f(x) = 2x³ - 7x² - 5x + 4
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Say that a certain stadium for professional football has 70,000 seats. What is the shape of the
supply curve for tickets to football games at that stadium? Explain.
Answers
Answer: The shape of the supply curve for tickets to football games at the stadium with 70,000 seats is upward-sloping. This means that as the price of tickets increases, the quantity of tickets supplied also increases.
The reasoning behind this is simple: when the price of tickets is high, there is more incentive for the sellers (e.g. the stadium, ticket resellers, etc.) to sell more tickets. They have the ability to supply more tickets as the demand for tickets at the high price is likely to be higher, thus increasing their profits.
However, it is important to note that the upward slope of the supply curve is not necessarily linear. The supply curve for tickets to football games is likely to be more elastic in the higher price range, meaning that as the price continues to increase, the quantity supplied may increase at a slower rate. This is because at some point, even if the price continues to rise, there will be a limit to how many tickets can actually be sold due to a decrease in demand.
Overall, the upward-sloping shape of the supply curve for tickets to football games at the stadium with 70,000 seats reflects the basic principle of supply and demand: as the price increases, the quantity supplied will also increase, but at some point, the increase in price will lead to a decrease in demand, limiting the quantity supplied.
Step-by-step explanation:
What is the answer
? I’ve been having triuble
Answers
Answer:
120°
Step-by-step explanation:
We need to find the missing angle <SRM
The angles inside a triangle always add up to 180°. So this means:
<TSR+<STR+<TRS=180°
65°+55°+<TRS=180°
120°+<TRS=180°
<TRS=180°-120°=60°
All angles along a straight line add up to 180°. This means:
<TRS+<SRM=180°
60°+<SRM=180°
<SRM=180°-60°=120°
Answer:
120° is the answer please mark. brainly
Classify the following triangle. Check all that apply.
A. Right
• B. Acute
C. Scalene
• D. Obtuse
•E. Isosceles
• F. Equilateral
Answers
Answer:
Right, Isosceles
Step-by-step explanation:
The little square in the corner means its right angled, so a right triangle. This also means that it cannot be acute or obtuse.
The two hash marks shows two sides are the same. So it is isosceles. This also means it cannot be scalene or equilateral.
Find the exact value of x
Answers
Step-by-step explanation:
answer, verified answer
A disc is rolled thrice what is the probability
Answers
Probability of an event = (number of favorable event) / (total number of event).
P(B) = (Event B) / (total number of event).
Probability of getting 1 = 1/6.
Rolling dice is an independent event, it is not dependent on how many times it’s been rolled.
Probability of getting 1 three times in a row = probability of getting 1 first time × probability of getting 1 second time × probability of getting 1 third time.
Probability of getting 1 three times in a row = (1/6) × (1/6) × (1/6) = 1/216.
Hence, the probability of getting 1 three times in a row is 0.463%.
Let h(x) = (gof)(x)=√x+3
Which of the following could be a possible decomposition of h(x)?
A. f(x)=√x; g(x)=x+3
B. f(x)=x; g(x)=x+3
c. f(x)=x+3; g(x)=√x
D. f(x)=3x; g(x)=√x
Answers
Answer:
the correct answer is letter A
